Even answers

Section 1.1

2.
a) true
b) not a statement
c) false
d) not a statement

4.
a) Some people like me.
b) Angle 1 is not a right angle.

6. conjunction

8. disjunction

10. conditional

12.
hypothesis: "two chords of a circle have equal lengths"
conclusion: "the arcs of the chords are congruent"

34. Segments AM and segments MB have the same length.

38. Andy is a naughty boy.

44. No conclusion (invalid use of the Law of Detachment)

Section 1.2

2. The measure of angle ABC is less than 90°, while the degree measure of angle EDF is larger than 90°.

4. No.

6. 3 lines

8. *Any* of these measures, although in Geometry class, we tend to stick to angles between 0° and 180°.

10. A-X-B

36. 14

38. x + y

40. measure of angle 1 is 120°

42. 34°

44. x + y

46. see. p. 16 for construction

Section 1.3

2. midpoint

4. 4 feet 4 inches

8. 90 seconds

10. a. infinite b. one c. none d. none

12. a. no difference b. no difference c. no difference
d. the first is the ray starting at C and passing through D while the second is the ray starting at D and passing through C.

14. a. False b. False c. True d. True e. False

16. x = 8 and AB = 36

18. No; Yes; Yes; No

28. a. Equal b. Equal c. AC is twice DC

Section 1.4

2. a. obtuse b. straight c. acute

4. a. congruent b. none

6. vertical

8. supplementary

10. a. True b. False c. False d. False e. True

12. B is not in the interior of angle FAE, so the Angle-Addition Postulate does not apply.

14. a. x + y = 180 b. x = y

16. 62°

18. x = 12

20. x = 8; measure of angle RSV is 69°

22. x = 14; y = 4

24. 39° and 51°

26. a. (90 – x)° b. (102 – 3x)° c. (90 – 2x – 5y)°

28. x = 131

Probability Quiz

1. Neither
2. Conditional
3. Neither
4. Conditional
5. Neither
6. 1/36
7. 5/36
8. 1/6
9. 4/13
10. 11/26
11. 2/13
12. 169/329
13. 160/329
14. 0
15. 2/5

Angle Measuring Worksheet

1. 38°
2. 94°
3. 167°
4. 99°
5. 324°
1. K-Q-L, etc.
2. P, Q, L, etc.
3. S
4. ray RQ
5. ray RQ and ray RL
6. Q
7. angle PRQ and angle QRP
8. a. acute b. straight c. right d. right e. adjacent
9. angle PQJ
10. 35°
11. 8
12. 85°
13. 45°
14. 9
15. 1
16. ZI, OI
17. True
18. False
19. False
20. True

Section 1.5

2. Either Substitution or Distributive [x + x = (1 + 1)x = 2x]
4. Addition Property of Equality
6. Addition Property of Equality
8. If the measures of 2 angles is 180°, then the angles are supplementary.
10. Definition of angle-bisector
12. AM = MB
14. measure of angle 1 = measure of angle 2 or angle 1 is congruent to angle 2
16. angle 1 and angle 2 are complementary
18. x = 7
20. 1/2 = 50%
22. x = -20
24.

1. Given
2. Subtraction Property of Equality
3. Division Property of Equality

Section 1.6

2.

1. Given
2. Definition of a straight angle
3. Angle Addition Postulate
4. Substitution
5. Given
6. Definition of a right angle
7. Substitution
8. Subtraction Property of Equality
9. Angle Addition Postulate
10. Substitution
11. Definition of complementary

4.

1. measure of angle AOB = measure of angle 1 and measure of angle BOC = measure of angle 1
2. measure of angle AOB = measure of angle BOC
3. angle AOB is congruent to angle BOC
4. ray OB bisects angle AOC

12.

1. Given
2. measure of angle 1 = measure of angle 2 and measure of angle 3 = measure of angle 4
3. Given
4. measure of angle 2 + measure of angle 3 = 90
5. Substitution
6. angles 1 and 4 are complementary

20. In space, there are an infinite number of lines perpendicular to a given line at a point on the line.
22. AE = AB + BC + CD + DE

Section 1.7

10. Drawing with line CD intersecting line AB at point E at 90°. Given angle AEC is a right angle. Prove line AB is perpendicular to line CD.
12. Drawing of angles 1 and 2 and angle 3 a supplement of angles 1 and 2. Given angle 1 is supplementary to angle 3 and angle 2 is supplementary to angle 3. Prove angle 1 is congruent to angle 2.

14. Drawing of angles 1 and 2, both right angles. Given angles 1 and 2 are right angles. Prove angle 1 is congruent to angle 2.
16. measure of angle 1 = 133°, measure of angle 3 = 133°, measure of angle 4 = 47°
18. x = 8; measure of angle 2 = 56°
20. x = 55; measure of angle 2 = 70°

Section 2.1

2. a. 109° b. 71°
4. a. 110.8° b. 110.8°
6. l is parallel to t
8. a. draw two parallelograms not intersecting b. draw two parallelograms intersecting at right angles

10. a. one b. one
12. a. 88° b. 92° c. 88°
14. x = 22.5 and the measure of angle 5 is 92°
16. x = 20; y = 10; measure of angle 8 is 110°
18. No
20.

1. Given
2. If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
3. If two lines intersect, the vertical angles are congruent.
4. m is parallel to n
5. If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
6. Angle 1 is congruent to angle 4; transitive property for congruence.

Section 2.2

2.
Converse: If x ≠ 0, then x > 2. FALSE
Inverse: If x not greater than 2, then x = 0. FALSE
Contrapositive: If x = 0, then x is not greater than 2. TRUE
6. Triangles ABC and DEF are not congruent.

Section 2.3

2. l parallel to m
4. cannot be determined
6. cannot be determined
8. none
10. l parallel to n
12. l parallel to n
14. l parallel to m
16. p parallel to q
18.
1.Given
2. If two parallel lines are cut by a transversal, then the corresponding angles are congruent
4. Angles 3 and 4 are congruent
6. l is parallel to n; If two linees are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
24. x = 18
26. x = 140

Section 2.4

2. 59°
16. x = 108°, y = 44°, z = 47°
18. 108°
20. x
22. x = 7
24. x = 8

Section 2.5

2. decrease
4. 118°
8. a. 720° b. 1080°
10. a. 120° b. 144°
12. a. 60° b. 36°
14. a. 13 b. 15
16. a. 12 sides b. 30 sides
18. a. 8 b. 40
20. 72°
28.

1. Regular hexagon ABCDEF with diagonal segment AC and external angle 1; given.
2. Extend segment BC through B to a point H; a line can be extended infinitely.
3. measure of angle ABH = measure of angle 1; the exterior angles of a regular polygon are of equal measure.
4. measure of angle ABH = measure of angle 2 + measure of angle 3; the measure of an exterior angle of a triangle equals the sum of the measures of the nonadjacent interior angles.
5. measure of angle 2 + measure of angle 3 = measure of angle 1; substitution.

32. a. 180 – (n – 2)*180/n b. 360/n
40. Draw BC in the concave quadrilateral ABCD. Since the sum of the angle measures in each of the two triangles formed is 180°, the sum of the interior angle measures of the quadrilateral must equal 180° times 2 or 360°.

Section 3.1

2. a = 10; b = 8; c = 11
4. measure of angle E is 38°
6. triangle BCA is congruent to triangle EDF
10. ASA
12. SAS
14. SAS
16. SAS
18. ASA
20.
a. segment MP is congruent to segment MP (Reflexive Property aka Identity);
b. SSS

Section 3.1 cont.

22. angle WVY congruent to angle ZVX
24. angle E congruent to angle J
26.

1. Given
2. If 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent.
3. segment AD is parallel to segment BC
4. angle DAC is congruent to angle BCA
5. Identity (Reflexive Property)
6. triangle ABC is congruent to triangle CDA

34. No- not congruent.
36. Yes; AAS.

Section 3.2

10. measure of angle 1 = 39°measure of angle 2 = 51°; measure of angle 3 = 51°; measure of angle 4 = 39°; measure of angle 5 = 39°; measure of angle 6 = 39°;
12.

1. ray HJ bisects angle KHL
2. If a ray bisects an angle, it forms 2 congruent angles
3. Given
4. If two lines are perpendicular, then they form congruent adjacent angles.
5. segment HJ is to segment HJ
6. triangle HJK is congruent to triangle HJL
7. CPCTC

Section 3.3

2. angle T is congruent to angle U
4. 28
14. determined
16. overdetermined
24. 90 + x

Section 3.5

4. False
6. True
14. a. Not possible; b. Not possible; c. Possible
18. Isosceles acute triangle
24. Salina

Section 4.1

10. Angle B
14. False
25.

Section 4.2

2. a) no b) no
4) Kite
6) a) Kite b) Congruent
8) Segment YW
10) 15.3
12) a) 16 b) 20 c) 12
14) 25.4
16) a) no b) yes
18) Bisect each other
20) 1-Quad. ABCD with midpoints E, F, G, and H of the sides 3-The segment that joins the midpoints of two sides of a triangle is parallel to the third side of the triangle 4- segment EF is parallel to segment HG
22.

24.

26.

28.

30) 2, 9, 18

Section 4.3

page 201 8-30 Even

8. CD=5; AD=12; AC=13
10. x=7; y=3
12. NQ= cquare root of 117; MP= square root of 117
14. MQ=8; NP=8
16. AB=square root of 61
18. BC=square root of 74
20. 5
22. True
24. 1) Rect. WXYZ with diagnols WY and XZ
2) WY is congruent XZ
4) Identity
5) SSS
6) <1 is congruent<2; CPCTC
26. b
28. x=6 P=4(6)=24
30. A rhombus is a parallelogram with adjacent sides congruent. Since a parallelogram has opposite sides congruent, then all the sides of a rhombus must be congruent.

Section 4.4

12. AB = 5.1
14. x = 3
16. 2x + 4y +1
17.

18.

20. WX = 33

Practice Midterm

solutions

Section 5.1

2) a) 5/9
b) 6/13
c) 20 oz/32 oz=8/5
d) 32 oz/20 oz=5/8

4) a) 3/4
b) 12in/72in=1/6
c) 150cm/200cm=3/4
d) 1 gal/24 miles is in-commensurable

6) a) x=7
b) x=4

8) a) x=+or-12
b) x=+ or 8

10) a) x=-7 or x=4
b) x=+ or -8

12) a) x=+ or - square root of 15
b) x= (1+or-square root of 69)/2

14) a) There is no solution
b) x squared cannot equal a negative # therefore there is no solution.

16) 13 1/3 divided by 4 = 3 1/3 yards for each dress

18) x=192 worksheets

20) approximately 6 copy machines

22) a) ADis approx square root of 96 or 4squareroot 6 or 9.80
b) DC=8 1/3

24) x=24 angles are 48 degrees, 72 degrees, 96 degrees, and 144 degrees.

26) 40 and 140 degrees.

Section 5.2

2 a) No b) Yes
4) a) No b) Yes
6) a) Angle C b) XN
8) ABCDE is similar MNPQR
10) a) measure of Angle B=23 degrees
b) measure angle RPC=67 degrees
c) AC=10
d) CB=24
12) a) Symmetric b) Transitive c) Reflexive
14) HJ=3 3/4
16) x=64 degrees
18) HK=15
20) Parallelograms
22) AB=x+8=13 1/3+8=21 1/3
24) AE= negative 2 + 2square root19 which is approximately 6.72
26) x=56/5
28) x=15/7=2 1/7 in.
30) x=38 2/5 The kite is 38 2/5 feet above the ground.

Section 5.3

14) 1-Given 3-Substitution 4-Identity 5-SAS
24) DE=5

Section 5.4

2) TV/SV=SV/VR
4) TR/TS=TS/TV
6) RT=9
8) a) DE=12 b) DE=6
10) a) DF=13 b) DF is approximately 13.42
12) a) Yes b) No c) Yes d) No
14) a) Right Triangle b) Right Triangle c) Obtuse Triangle d) Obtuse Triangle
16) x=50 ft
18) x=20 ft
20) x=32 ft

Section 5.5

2) a) AC=1 b) BC=1
4) a) XZ=a b) YZ=a square root of 3
6) XZ=YZ=5square root of 2 or approx 7.07
8) XZ=12; YZ=12
10) ED=6; FD=6square root of 3 or approx 10.39
12) DE= 6square root of 3 or approx 10.39 and DF=18
14) RS=3square root of 2 or approx 4.24 and ST= approx 7.35
16) PM=PN=10
18) ZW= approx 5.2 or 3square root of 3

Section 5.4 in class work

26) x=square root of 50=5 square root of 2
28) MB=square root of 73
38) Length of each side is 12; therefore perimeter is 48

Section 5.6

2) x=12; 24g of chem A, 12g of chem B, 36g of chem C
4) a) No b) Yes
6) FG=4 2/7 GH=3 3/7, EH=13 5/7
8) x=7 or x+-5
BC=7; DE=5
10) EC=12 1/2
12) a=9 or a=2 EC=24 or EC=3
14) a) Yes b) No
16) WT=3 6/7

Section 6.2

4) angle RT=36 degrees
8) a) angle A=54 degrees; b) angle ABC=63 degrees; c) angle ACB=63 degrees
10) a) angle AB=110 degrees; b) angle 2=38 degrees
12) a) angle RT=138 degrees; b) angle RST=222 degrees
14) angle RS=96 degrees
16) angle CE=104 degrees; angle BD=38 degrees
18) a) Supplementary; b) 68 degrees
22) 1. Given; 2. If 2 parallel lines are cut by a transversal, then the alt. int. angles are congruent
3.angle S=angle T 4. The measure of an inscribed angle is 1/2 the arc measure 5. same as 4
6. Substitution 8. arc RT is congruent to arc SQ
28) approx 38,131 feet or 11 miles

Unit 7 IW #2

solutions

Unit 7 IW #3

solutions

Unit 7 IW #4

p. 397
18. One million
20. V = 160 cubic inches; T = 232 square inches
22. width of the base is 5 meters; length of the base is 7 meters

p. 407
6. a. V b. segments MN, NP, PQ, QR, RS, SM c. Yes d. Yes
8. a. 7 b. 12 c. 7
10. T = 161.6 square cm
16. a. slant height b. lateral edge
20. a. 111.24 square inches b. 172.74 square inches

Unit 7 IW #5

p. 417
6. 37.55 cubic inches
14. 6.5 feet

p. 427
14. SA = 452.39 square inches V = 904.79 cubic inches

Unit 8 IW #3

p. 466

Unit 9 IW #2

solutions

Unit 9 IW #5

p. 512
30. 394.4 feet
32. 90°

Unit 9 IW #6

solutions